Let us assign the name Tes letters to the letters of the word test i.e. t,e,s.
Consider the quantity P of Tes letters as percentage of the word's length.
Thus P(set)= 100%
P(best)=75%
P(resistor)=50%

P(settee)=100%
P(estimates)=66% etc
If Pmx(n) represents the maximal value of P for a word of n letters, - there exist trivial samples for n=3,4,5,6,7 i.e. set,test,tests,settee,settees - they all comply with Pmx(n)=1.

Please provide the values of Pmx for words of 8,9, ....20 letters.

Elligible: words appearing in reputable dictionary, including derivatives like plurals, verbs in 3rd person et al.